Certainly! Let's work through each part of the problem step by step to find the solutions.
### Part e)
Evaluate [tex]\(\left(\frac{2}{5} \times \frac{3}{4} \times \frac{5}{6}\right)^2\)[/tex]:
1. First, multiply the fractions:
[tex]\[
\frac{2}{5} \times \frac{3}{4} \times \frac{5}{6}
\][/tex]
2. Multiply the numerators:
[tex]\[
2 \times 3 \times 5 = 30
\][/tex]
3. Multiply the denominators:
[tex]\[
5 \times 4 \times 6 = 120
\][/tex]
4. Simplify the fraction:
[tex]\[
\frac{30}{120} = \frac{1}{4}
\][/tex]
5. Now, square the result:
[tex]\[
\left(\frac{1}{4}\right)^2 = \frac{1}{16}
\][/tex]
6. Evaluate [tex]\( \frac{1}{16} \)[/tex]:
[tex]\[
\frac{1}{16} = 0.0625
\][/tex]
So the answer for Part e) is [tex]\(0.0625\)[/tex].
### Part 1)
Evaluate [tex]\(\frac{6}{7} - \frac{4}{5}\)[/tex]:
1. Find a common denominator for the fractions. The least common multiple of 7 and 5 is 35.
2. Convert each fraction to have this common denominator:
[tex]\[
\frac{6}{7} = \frac{6 \times 5}{7 \times 5} = \frac{30}{35}
\][/tex]
[tex]\[
\frac{4}{5} = \frac{4 \times 7}{5 \times 7} = \frac{28}{35}
\][/tex]
3. Subtract the second fraction from the first:
[tex]\[
\frac{30}{35} - \frac{28}{35} = \frac{30 - 28}{35} = \frac{2}{35}
\][/tex]
4. Evaluate [tex]\( \frac{2}{35} \)[/tex]:
[tex]\[
\frac{2}{35} \approx 0.05714285714285705
\][/tex]
So the answer for Part 1) is approximately [tex]\(0.0571\)[/tex].
### Part 9)
Evaluate [tex]\(-0.24\)[/tex]:
This part is straightforward as it’s just the number given. The answer for Part 9) is [tex]\(-0.24\)[/tex].
### Part h)
Evaluate [tex]\((\sqrt{2})^{-}\)[/tex]:
Given the expression, it is often understood as the reciprocal of [tex]\(\sqrt{2}\)[/tex]:
1. Calculate the reciprocal of [tex]\(\sqrt{2}\)[/tex]:
[tex]\[
\frac{1}{\sqrt{2}}
\][/tex]
2. Simplify using properties of square roots:
[tex]\[
\frac{1}{\sqrt{2}} = \frac{1}{2^{0.5}} = 2^{-0.5} = 2^{-0.5} = 0.7071067811865475
\][/tex]
So the answer for Part h) is approximately [tex]\(0.7071\)[/tex].
### Final Answers:
- Part e) [tex]\( = 0.0625 \)[/tex]
- Part 1) [tex]\( \approx 0.0571 \)[/tex]
- Part 9) [tex]\( = -0.24 \)[/tex]
- Part h) [tex]\( \approx 0.7071 \)[/tex]
